A few documents I wrote 1st year of PhD (2021-2022) My PhD thesis is on higher-order automata and related topics. Here is: The From profinite words to profinite $\lambda$-terms talk I gave the 4th of July 2022 at the Structure Meets Power workshop, Paris (abstract) The Profinite $\lambda$-terms and more talk I gave the 19th of May 2022 at the Duality and more workshop, Nice The Topology and Categories for higher-order automata talk I gave the 12th of April 2022 at MGS 2022, Nottingham Master internship (2021) I wrote things about canonical extensions, which were the topic of my M2 research internship from March 2021 to August 2021 under the supervision of Sam van Gool and Paul-André Melliès. You can find here the following documents: A presentation of linear logic-related applications of canonical extensions which I used during the ASV day on the 19th November. A truncated version of my internship defense slides that I used during the PPS day, the 13th October. The presentation used for the internship defense on the 3th of September. The report, respecting the 20 pages limit and sent on the 20th of August.